even for the frequentist, and that’s what we make decisions with, so focusing on p(x) is a bit of misdirection. The whole frequentist-vs-bayesian culture war is fake. They’re both perfectly consistent with well defined questions. (They have to be, because math works.)
And yes to everything else, except...
As to whether god plays dice with the universe… that is not in the scope of probability theory. It’s math. Your Bayesian is really a pragmatist, and your frequentist is a straw person.